FLAT LIKELIHOODS: THE SKEW NORMAL DISTRIBUTION CASE

Several references argue in favor of alternative estimation methods, rather than the likelihood one, when the likelihood function exhibits flat regions. However, in the case of the skew normal distribution we present a discussion describing the interpretation of those flat likelihoods. This distribution is widely used in several interesting applications and contains the normal distribution as a nested model and the half-normal as an embedded model. Here, we show that flat likelihoods provide relevant information that should be carefully analyzed before discarding its use and proposing other estimation methods. Two well-known examples, that have been reported as troublesome, are analyzed here, including also an exhaustive computational study. The analysis of different scenarios allows to understand not only the reason of this likelihood function shape, but also to discover the information this behavior provides.